





'''simple docstring'''



import random




def  _lowerCAmelCase    (					lowerCamelCase_      :	int					):
			__lowercase					    =				num - 1
			__lowercase					    =				0

			while s % 2 == 0:
						__lowercase					    =				s // 2
						t += 1

			for _ in range(5					):
						__lowercase					    =				random.randrange(2		,							num - 1					)
						__lowercase					    =				pow(UpperCamelCase_		,							UpperCamelCase_		,							UpperCamelCase_					)
						if v != 1:
									__lowercase					    =				0
									while v != (num - 1):
												if i == t - 1:
															return False
												else:
															__lowercase					    =				i + 1
															__lowercase					    =				(v**2) % num
			return True




def  _lowerCAmelCase    (					lowerCamelCase_      :	int					):
			if num < 2:
						return False

			__lowercase					    =				[
			    2,
			    3,
			    5,
			    7,
			    1_1,
			    1_3,
			    1_7,
			    1_9,
			    2_3,
			    2_9,
			    3_1,
			    3_7,
			    4_1,
			    4_3,
			    4_7,
			    5_3,
			    5_9,
			    6_1,
			    6_7,
			    7_1,
			    7_3,
			    7_9,
			    8_3,
			    8_9,
			    9_7,
			    1_0_1,
			    1_0_3,
			    1_0_7,
			    1_0_9,
			    1_1_3,
			    1_2_7,
			    1_3_1,
			    1_3_7,
			    1_3_9,
			    1_4_9,
			    1_5_1,
			    1_5_7,
			    1_6_3,
			    1_6_7,
			    1_7_3,
			    1_7_9,
			    1_8_1,
			    1_9_1,
			    1_9_3,
			    1_9_7,
			    1_9_9,
			    2_1_1,
			    2_2_3,
			    2_2_7,
			    2_2_9,
			    2_3_3,
			    2_3_9,
			    2_4_1,
			    2_5_1,
			    2_5_7,
			    2_6_3,
			    2_6_9,
			    2_7_1,
			    2_7_7,
			    2_8_1,
			    2_8_3,
			    2_9_3,
			    3_0_7,
			    3_1_1,
			    3_1_3,
			    3_1_7,
			    3_3_1,
			    3_3_7,
			    3_4_7,
			    3_4_9,
			    3_5_3,
			    3_5_9,
			    3_6_7,
			    3_7_3,
			    3_7_9,
			    3_8_3,
			    3_8_9,
			    3_9_7,
			    4_0_1,
			    4_0_9,
			    4_1_9,
			    4_2_1,
			    4_3_1,
			    4_3_3,
			    4_3_9,
			    4_4_3,
			    4_4_9,
			    4_5_7,
			    4_6_1,
			    4_6_3,
			    4_6_7,
			    4_7_9,
			    4_8_7,
			    4_9_1,
			    4_9_9,
			    5_0_3,
			    5_0_9,
			    5_2_1,
			    5_2_3,
			    5_4_1,
			    5_4_7,
			    5_5_7,
			    5_6_3,
			    5_6_9,
			    5_7_1,
			    5_7_7,
			    5_8_7,
			    5_9_3,
			    5_9_9,
			    6_0_1,
			    6_0_7,
			    6_1_3,
			    6_1_7,
			    6_1_9,
			    6_3_1,
			    6_4_1,
			    6_4_3,
			    6_4_7,
			    6_5_3,
			    6_5_9,
			    6_6_1,
			    6_7_3,
			    6_7_7,
			    6_8_3,
			    6_9_1,
			    7_0_1,
			    7_0_9,
			    7_1_9,
			    7_2_7,
			    7_3_3,
			    7_3_9,
			    7_4_3,
			    7_5_1,
			    7_5_7,
			    7_6_1,
			    7_6_9,
			    7_7_3,
			    7_8_7,
			    7_9_7,
			    8_0_9,
			    8_1_1,
			    8_2_1,
			    8_2_3,
			    8_2_7,
			    8_2_9,
			    8_3_9,
			    8_5_3,
			    8_5_7,
			    8_5_9,
			    8_6_3,
			    8_7_7,
			    8_8_1,
			    8_8_3,
			    8_8_7,
			    9_0_7,
			    9_1_1,
			    9_1_9,
			    9_2_9,
			    9_3_7,
			    9_4_1,
			    9_4_7,
			    9_5_3,
			    9_6_7,
			    9_7_1,
			    9_7_7,
			    9_8_3,
			    9_9_1,
			    9_9_7,
			]

			if num in low_primes:
						return True

			for prime in low_primes:
						if (num % prime) == 0:
									return False

			return rabin_miller(UpperCamelCase_					)




def  _lowerCAmelCase    (					lowerCamelCase_      :	int = 1_0_2_4					):
			while True:
						__lowercase					    =				random.randrange(2 ** (keysize - 1)		,							2 ** (keysize)					)
						if is_prime_low_num(UpperCamelCase_					):
									return num


if __name__ == "__main__":
	_SCREAMING_SNAKE_CASE       =     generate_large_prime()
	print(('''Prime number:''', num))
	print(('''is_prime_low_num:''', is_prime_low_num(num)))










'''simple docstring'''

from __future__ import annotations

SCREAMING_SNAKE_CASE__     :						List[Any]	=  1.6021e-19  # units = C






def 				a  (     UpperCamelCase_    :    float      ,					UpperCamelCase_    :    float      ,					UpperCamelCase_    :    float      ,					)       ->	tuple[str, float]:
		if (conductivity, electron_conc, mobility).count(0			) != 1:
				raise ValueError('You cannot supply more or less than 2 values'			)
		elif conductivity < 0:
				raise ValueError('Conductivity cannot be negative'			)
		elif electron_conc < 0:
				raise ValueError('Electron concentration cannot be negative'			)
		elif mobility < 0:
				raise ValueError('mobility cannot be negative'			)
		elif conductivity == 0:
				return (
				    "conductivity",
				    mobility * electron_conc * ELECTRON_CHARGE,
				)
		elif electron_conc == 0:
				return (
				    "electron_conc",
				    conductivity / (mobility * ELECTRON_CHARGE),
				)
		else:
				return (
				    "mobility",
				    conductivity / (electron_conc * ELECTRON_CHARGE),
				)


if __name__ == "__main__":
			import doctest

			doctest.testmod()




